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altered by this change of temperature, and, as the length of the day is 86,400 seconds, this length would, by this means, be decreased nearly one second. This change of dimensions would not affect the earth's mass, or its attraction on the moon, and the absolute time of the moon's periodical revolution, which is nearly 27 days, would not be altered; but, being measured by days, which have decreased in length nearly one second, that period would appear longer by 27 times that decrement, or 23 seconds; so that if the earth's temperature had decreased one degree since the time of Hipparchus, the moon's periodical revolution about the earth would appear to have increased 23 seconds. Now, it has been found, by observation, after allowing for the acceleration of moon's motion, arising from the secular change in the eccentricity of the earth's orbit, that the periodic time of revolution has not suffered any perceptible change, since the earliest observations on record; therefore no change of temperature, of any moment, could have taken place in the earth during that period.
The theory, combined with astronomical observations, has done more for the determination of the figure of the earth, than the actual measures of the degrees of the meridian, which have been made in several countries, with great labor and expense, but without obtaining that degree of accuracy, which was reasonably to have been expected. The degree measured in Lapland, by Maupertuis and his associates, has been found more than two hundred toises too great, by the late measurement of Svanberg.* The degree of Austria, by Liesganig, has been proved by Baron de Žach to be so very inaccurate, as to be wholly undeserving of notice. The measures at the Cape of Good Hope, Peru, and Pennsylvania, are considered tolerably accurate, but not of the first order. The late ones in France and England have
* The discovery of this mistake would have mortified extremely the vanity of Maupertuis, who, upon his return from this northern expedition, published immediately an account of it, without waiting to know the result of the operations in Peru, wishing to appropriate to himself the whole honor of the operations, to which, in fact, he had contributed but a small portion. He also caused a portrait of himself to be engraved, in a Lapland dress, with his hand resting upon the northern part of a terrestrial globe, as if he was compressing it, and for some time he was called by his countrymen, ' l'aplatisseur de la terre ;' (the flattener of the earth ;) instead of giving the
surpassed all others in the accuracy of the instruments, and precautions of the observers; but even these, particularly the English measurement, have not escaped animadversion, on account of their discrepancies. The most probable combination of these measures, shows that the oblateness of the earth is between zoo and tio, agreeing with the results of the lunar theory. It may also be observed, that this oblateness being less than zio, proves by Clairaut's theorem, beforementioned, that the earth increases in density from the surface towards the centre, confirming the proof deduced before from other sources.
The precession of the equinoxes is intimately connected with the theory of the earth, and the oblateness of its form. Newton was the first who discovered its cause, and that, in his hypothesis of a homogeneous earth, it was produced by the attraction of the sun and moon upon the protuberant matter or excess above a sphere, supposed to be described about the polar diameter. The calculation of the precession, by the theory of gravity, is one of the most difficult of all the celestial phenomena, and the one which has been the most fruitful in mistakes. Newton's calculations for a homogeneous ellipsoid, in the Principia, contained important errors in principles and in data. These remained without detection till the year 1749, above sixty years after its publication, when D'Alembert first gave the true principles of solution in his Recherches sur la Précession des Equinoxes.' The general results of his solution have been confirmed by the calculations of Euler, Lagrange, and Laplace, and are now universally admitted to be true. D'Alembert proved in this work, that the sun's attraction would produce double the precession, which Newton had calculated, and that this mistake was nearly balanced by another in his data, in taking the moon's disturbing force considerably greater than its true value. Several other astronomers and mathematicians have since written
glory to Newton, who had proved forty years before, from the theory, that it must be flattened. Voltaire, who was then the friend of Maupertuis, wrote the four following lines, placed at the bottom of this portrait.
"Ce globe mal connu, qu'il a su mesurer
De lui plaire et de l'éclairer.' Voltaire, at a subsequent period, when addressing himself to the members of the Academy who composed the northern expedition, says with more justice,
Vous avez récherché, dans ces lieux plein d'ennui,
upon this subject with various success. Bevis, Silvabella, Walmsey, Milner, Simpson, Landen, La Lande, and Robertson, have not proceeded upon correct principles. Several of them, like La Lande, adopted Simpson's erroneous method. D'Alembert, rather vexed to find La Lande had placed his solution upon a par with Simpson's, remarked, with some testiness; 'Le fameux problême de la Précession des équinoxes, dont J'ai donné le premier la solution en 1749, a été depuis bien ou mal résolu par beaucoup d'autres Géometres. M. de la Lande, dans un vaste Recueil qu'il a publié sous le titre d'Astronomie, n'ayant pas distingué celles de ces solutions, qui sont défecteuses d'avec celles qui ne le sont pas, s'est contenté de les indiquer toutes in globo, et de dire qu'elles ne sont pas d'accord.' Dr Horsley, in his edition of Newton's works, adopts the prudent course of not expressing his opinion, and though fond of giving his own notes, and in many cases where no commentary was necessary, in the part treating of the precession, he very unceremoniously turns the reader over to Euler and Simpson, not wishing to decide upon so difficult a point.
The theory of the tides, first explained by Newton, and afterwards by Maclaurin and Bernoulli, in their prize papers of 1740, has been fully examined by Laplace, in the fourth book of his Mécanique Céleste, and in a paper published in the Memoirs of the Academy of Arts and Sciences of Paris, for 1818. In these works he fully analyses all the effects of the change of distances, declinations, velocities or elongations of the sun and moon, and compares his theory with the observations made at Brest, during two successive periods of six and eight years ; giving analytical formulas for computing the times of the tides, their heights, and all the effects arising from the change of situation and distances of the sun and moon; the whole subject being treated very much in detail, and in a satisfactory manner.
* The following is Dr Horsely's note ;
Quem tamen longè alium invenerunt viri permagni Eulerus et Simpsonus nostras ; quos velim Lector consulas. Ipse nil definio. VOL. XX.-NO. 47.
Before closing this review, it may not be amiss to mention a few of the most noted works on astronomy, in which the state of the science, as it now exists, inay be sound. The Astronomie by La Lande, in 3 vols. 4to, third edition, 1792,* is complete up to the time of its publication. It contains a description of astronomical instruments, and the methods of reducing the observations, an account of the most noted European observatories, a good treatise of spherics, with most of the formulas, used in astronomical calculations, and a collection of tables of the motions of all the planets, particularly Delambre’s of the Sun, Saturn, Jupiter and its Satellites. This was the standard work to which astronomers referred for nearly half a century; nothing so complete had ever before been published. It contains a number of things that might as well have been omitted, but it is an extremely useful and interesting work for astronomers. Without having mathematical talents of the first order, La Lande, by his great zeal and devotion to astronomy, did much for its improvement. All parts of that science, which required no more than an accurate knowledge of spherics, and the elementary calculations of the perturbations of the motions of the planets, by their mutual attractions, were quite within the compass of his abilities; but when he attempted to explain and calculate the forces, which cause the precession of the equinoxes and the change of the inclinations of the lunar orbit, he laid himself open to the sneers of those, who, like D'Alembert, were offended with his excessive egotism. This foible in La Lande's character was carried to a great excess.
It is to be seen in his Bibliographie, at every moment. In mentioning the year 1732, he remarks, 'Cette année, qui est celle de ma naissance, est remarquable pour l'astronomie.' In speaking of his astronomy he says, 'il a été utile en formant presque tous les astronomes qui existent actuellement.' He could bear the most fulsome flattery. His bust, made of Carrarian marble, having been placed in an Italian observatory, mention was made of it in a printed letter, in which it was called il dio dell' astronomia, (the God of Astronomy.) He thought the compliment rather extravagant, but was, notwithstanding, very much delighted with it. This weakness was, however, useful to astronomy.
* There was also a fourth volume relative to the tides at Brest, which was not republished with the third edition.
It induced him to keep up a correspondence with men of science in all parts of the world, and made him, for many years, the centre of information on all astronomical subjects.
The Complete System of Astronomy,' by Professor Vince, in 3 vols. 4to, 1797, 1799, and 1808, contains much useful matter, but it must be acknowledged, that it bears many marks of a crude compilation, particularly in the tables, in some of which the anomaly is counted from the aphelion, in others from the perihelion, some have all the corrections additive, others not; being copied from the works of La Lande, Delambre, and Burg, in the forms in which they were published, without taking the trouble to make much alteration, except in adapting them to the meridian of Greenwich. This mixture of different forms and systems, in the same collection of tables, may frequently lead to error, and it is to be regretted that Professor Vince did not adopt some fixed plan, and carry it fully through. The ease with which the use of the signs plus and minus is avoided in the solar tables, published by Delambre, and in those of Jupiter and Saturn, by Bouvard, makes the defect of Professor Vince's tables very apparent. Several parts of the translation of the introduction to his copy of Burg's tables are difficult to understand, without referring to the original work published by Delainbre, the translation being quite imperfect and filled with errors.
Notwithstanding these defects, the work is valuable for its extensive compilation of tables of the motions of the heavenly bodies, the catalogues of the fixed stars, and the numerous auxiliary tables for facilitating most of the calculations of the practical astronomer.
The Astronomie Théorique et Pratique,' by Delambre, in 1814, 3 vols. 4to, is an excellent work, but deficient in tables. All the instruments are described with the most approved methods of rectification. One of his chapters contains a good treatise on spherical trigonometry and the differential analogies, so useful in all branches of astronomy. It abounds with numerous formulas for the calculation of the effects of refraction, parallax, aberration, nutation, &c. His demonstrations are easy to follow, being quite full, without